The long-term objective of this research is to design, build and commercialize a medical imaging system based on Electrical Impedance Tomography (EIT). EIT is an attractive diagnostic tool due in part to its low-cost but more so because it differentiates tissue according to its electrochemical properties as opposed, say tissue density alone. In the past, the difficulty with EIT has been in obtaining adequate resolution. The first significant advance in resolution resulted from the work of Barber and Brown who drew the analogy between the inverse problem of EIT and that of CT/MRI and proposed the use of filtered backprojection of the Radon Transform. This advance resulted in the first commercially marketed EIT systems. In this proposal we show that their formula for inversion was correctly inspired but incorrectly implemented and it is properly understood to be an approximation to the true solution. We have obtained the exact inversion formula for their model and as such we are optimistic that it will mark the next advance in the resolution problem. The proposed research aims at implementing numerical algorithms based on this formula and also employing new nonlinear image enhancement algorithms which yield optimal noise-reduction parametrized by resolution.